Colossal magnetoresistivity (CMR) is caused by a magnetic field-induced insulator-to-metal transition. It is arguably one of the most dramatic phenomena that occur in solids due to competing forces in a complex system. In the CMR oxides the electron-phonon coupling and spin correlations that favor charge localization are competing against the electron kinetic energy and lattice elasticity that prefer charge delocalization. The CMR phenomenon occurs at the crossover point of charge-localized (insulating) and charge-delocalized (metallic) states, where the system is particularly susceptible to external stimuli such as a magnetic field. The competitions among these forces are usually considered globally as volume averages. However, since the system is complex and the phenomenon is non-linear, local fluctuations dominate the behavior of the system near the critical point. Therefore the system would appear spatially inhomogeneous if the measurement is made with certain time and length scales. To characterize and understand such a system it is required to deploy local approaches in which the competing interactions are evaluated locally. Experimentally, the pulsed neutron pair-density function (PDF) analysis is one of the methods of local structural study. Using the PDF technique it is suggested that the phase transition occurs via local and percolative processes. Also through the analysis of the local structure it is shown that the ionic size effect on the CMR phenomenon is not caused by a change in the band width as is usually assumed, but is due to local structural changes that affect polaron stability. The critical ionic size determined by this approach is in excellent agreement with experimental observations. The PDF results also indicate that the local structure of layered manganites is close to that of perovskite, suggesting that they share common elements of the CMR mechanisms.